Abstract
The appropriate choice of a threshold level, which separates the tails of the probability distribution of a random variable from its middle part, is considered to be a very complex and challenging task. This paper provides an empirical study on various methods of the optimal tail selection in risk measurement. The results indicate which method may be useful in practice for investors and financial and regulatory institutions. Some methods that perform well in simulation studies, based on theoretical distributions, may not perform well when real data are in use. We analyze twelve methods with different parameters for forty-eight world indices using returns from the period of 2000–Q1 2020 and four sub-periods. The research objective is to compare the methods and to identify those which can be recognized as useful in risk measurement. The results suggest that only four tail selection methods, i.e., the Path Stability algorithm, the minimization of the Asymptotic Mean Squared Error approach, the automated Eyeball method with carefully selected tuning parameters and the Hall single bootstrap procedure may be useful in practical applications.
Highlights
Extreme value theory (EVT) is a branch of statistics dealing with extreme values.It focuses on the asymptotic behavior of extreme values of random variables instead of the whole distribution
The selection of the threshold which separates the tail from the middle part of a return distribution is crucial in the estimation of tail-related risk measures
The right threshold is unknown in empirical applications
Summary
Extreme value theory (EVT) is a branch of statistics dealing with extreme values. It focuses on the asymptotic behavior of extreme values of random variables instead of the whole distribution. A frequently used procedure relies on the analysis of a mean excess plot, which represents the mean of the excesses of the threshold u This method was applied in Aboura (2014), Cifter (2011), Gilli and Këllezi (2006), Łuczak and Just (2020) and. The graphical-based threshold choice procedures require identification of stable regions in the graphs; they are highly subjective and difficult to apply in empirical studies. This paper provides an empirical study on various methods of optimal tail selection in risk measurement. We analyze twelve automatic methods of threshold selection. Some of these methods estimate a threshold at a very high level to estimate these risk measures at the recommended confidence levels.
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